Calculation of the Thermal Stresses in an Elastoplastic Plate Heated by Local Heat Source

Authors: M. Khaing, A. V. Tkacheva

Abstract:

The work is devoted to solving the problem of temperature stresses, caused by the heating point of the round plate. The plate is made of elastoplastic material, so the Prandtl-Reis model is used. A piecewise-linear condition of the Ishlinsky-Ivlev flow is taken as the loading surface, in which the yield stress depends on the temperature. Piecewise-linear conditions (Treska or Ishlinsky-Ivlev), in contrast to the Mises condition, make it possible to obtain solutions of the equilibrium equation in an analytical form. In the problem under consideration, using the conditions of Tresca, it is impossible to obtain a solution. This is due to the fact that the equation of equilibrium ceases to be satisfied when the two Tresca conditions are fulfilled at once. Using the conditions of plastic flow Ishlinsky-Ivlev allows one to solve the problem. At the same time, there are also no solutions on the edge of the Ishlinsky-Ivlev hexagon in the plane-stressed state. Therefore, the authors of the article propose to jump from the edge to the edge of the mine edge, which gives an opportunity to obtain an analytical solution. At the same time, there is also no solution on the edge of the Ishlinsky-Ivlev hexagon in a plane stressed state; therefore, in this paper, the authors of the article propose to jump from the side to the side of the mine edge, which gives an opportunity to receive an analytical solution. The paper compares solutions of the problem of plate thermal deformation. One of the solutions was obtained under the condition that the elastic moduli (Young's modulus, Poisson's ratio) which depend on temperature. The yield point is assumed to be parabolically temperature dependent. The main results of the comparisons are that the region of irreversible deformation is larger in the calculations obtained for solving the problem with constant elastic moduli. There is no repeated plastic flow in the solution of the problem with elastic moduli depending on temperature. The absolute value of the irreversible deformations is higher for the solution of the problem in which the elastic moduli are constant; there are also insignificant differences in the distribution of the residual stresses.

Keywords: Temperature stresses, elasticity, plasticity, Ishlinsky-Ivlev condition, plate, annular heating, elastic moduli.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1474375

References:

[1] Rykalin N. N. Calculations of thermal processes during welding. M.: Mashgiz,1951. 296 p.
[2] Sholokhov, MA Evaluation of the effect of the cutting shape and welding regimes on residual stresses in the hull structures of special equipment. (MA Sholokhov, A. S. Kurkin, S. I. Poloskov // Welding and Diagnostics. 2014. № 6. P. 5055.
[3] Bondar VS A variant of the theory of thermoplasticity. Bondar, V. V. Danshin, A. A. Kondratenko / Bulletin of the Peoples' Friendship University. Mechanics. - 2015. - No. 2. - P. 21-35.
[4] Sleptsova EA, Pavlov AR Determination of residual welding stresses and deformations during butt welding of thin plates. Bulletin of the SSU - Natural Science Series. - 2008. - №2 (61). - P. 273-287.
[5] Alexandrov SE, Lyamina EA, Novozhilova OV Influence of the yield stress on temperature on the stress state in a thin hollow disk. Problems of machine building and reliability of machines. 2013, №3. Pp. 43-48.
[6] Burenin A. A., Dats E. P., Murashkin E. V. Fomirovanie field of residual stresses under conditions of local thermal action, Izv. RAS MTT. 2014, No. 124-131.
[7] Investigation of the acoustic and resistive properties of promising chromo-margangane austenitic steels in the temperature range 5-300 K // LN Pal-Val, Yu. A. Semerenko, PP Pal-Val, LV Skibina, GN Grikurov / Condensed Media and Interphase Boundaries, Vol. 10, No. 3. - 2008. - P. 226-235.
[8] Toky N. V. Dependence of elasticity moduli of submicrocrystalline copper. Tokiy, V. V. Tokiy, A. N. Pilipenko, N. E. Pis'menova / Solid State Physics, 2014, Vol. 56, no. 5 pp. 966-969.
[9] Nadai A. Plasticity and destruction of solids. M: The world. - Т..2.- 1969.-864 p.
[10] Dats EP, Tkacheva AV, Shport RV The assembly of the ring-in-ring design by the method of hot landing // Bulletin of the Chelyabinsk State Pedagogical University. I.Ya. Yakovleva, series: the mechanics of the limiting state. 2014, No. 4 (22). P. 204-213.
[11] Burenin AA, Dats EP Tkacheva A. V. To the problem of mathematical simulation of the process of hot landing of cylindrical metal products // SibzhIM. Novosibirsk: From the Institute of SB RAS. 2014, Vol. 17 No. 3. P. 40 - 47.
[12] Bykovtsev GI, Ivlev D. D. Theory of plasticity. Vladivostok: The Dal'nauka. 1998.528p.